If a^{2}+b^{2}+c^{2}=a b+b c+a c then the value of \frac{a+c}{b}is

SSC CGL Tier II 21 Sep 2014 Paper

Question : 17 of 100

Marks: +1, -0

a^{2}+b^{2}+c^{2}=a b+b c+a c

then the value of

{a+c}/{b}

Solution:

(2)

a^{2}+b^{2}+c^{2}=a b+b c+c a

⇒a^{2}+b^{2}+c^{2}-a b-b c-c a=0

On multiplying by 2,

2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 b c-

2 c a=0

⇒ a^{2}+b^{2}-2 a b+b^{2}+c^{2}-2 b c

+c^{2}+a^{2}-2 a c=0

⇒(a-b)^{2}+(b-c)^{2}+(c-a)^{2}=0

⇒ a-b=0

⇒ a=b

b-c=0 ⇒ b=c

c-a=0 ⇒ c=a

∴{a+c}/{b}= {2 a}/{a}=2

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